Chandia, O., Bevilaqua, L. I., & Vallilo, B. C. (2014). AdS pure spinor superstring in constant backgrounds. J. High Energy Phys., (6), 16 pp.
Abstract: In this paper we study the pure spinor formulation of the superstring in AdS(5) x S5 around point particle solutions of the classical equations of motion. As a particular example we quantize the pure spinor string in the BMN background.

Chandia, O., Linch, W. D., & Vallilo, B. C. (2017). Master symmetry in the AdS(5) x S5 pure spinor string. J. High Energy Phys., (1), 15 pp.
Abstract: We lift the set of classical nonlocal symmetries recently studied by Klose, Loebbert, and Winkler in the context of Z(2) cosecs to the pure spinor description of the superstring in the AdS(5) x S5 background.

Chandia, O., Linch, W. D., & Vallilo, B. C. (2011). Compactification of the heterotic pure spinor superstring II. J. High Energy Phys., (10), 22 pp.
Abstract: We study compactifications of the heterotic pure spinor superstring to six and four dimensions focusing on two simple CalabiYau orbifolds. We show that the correct spectrum can be reproduced only if, in the twisted sector, there remain exactly 5 and 2 pure spinor components untwisted, respectively. This naturally defines a “small” Hilbert space of untwisted variables. We point out that the cohomology of the reduced differential on this small Hilbert space can be used to describe the states in the untwisted sector, provided certain auxiliary constraints are defined. In dimension six, the mismatch between the number of pure spinor components in the small Hilbert space and the number of components of a sixdimensional pure spinor is interpreted as providing the projective measure on the analytic subspace (in the projective description) of harmonic superspace.

Chandia, O., Mikhailov, A., & Vallilo, B. C. (2013). A construction of integrated vertex operator in the pure spinor sigmamodel in AdS(5) x S5. J. High Energy Phys., 2013(11), 11 pp.
Abstract: Vertex operators in string theory me in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the bghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinitedimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.

Chandia, O., & Vallilo, B. C. (2016). Onshell type II supergravity from the ambitwistor pure spinor string. Class. Quantum Gravity, 33(18), 9 pp.
Abstract: We obtain all the type II supergravity constraints in the pure spinor ambitwistor string by imposing consistency of local worldsheet gauge symmetries.

Chandia, O., & Vallilo, B. C. (2015). Nonminimal fields of the pure spinor string in general curved backgrounds. J. High Energy Phys., (2), 16 pp.
Abstract: We study the coupling of the nonminimal ghost fields of the pure spinor superstring in general curved backgrounds. The coupling is found solving the consistency relations from the nilpotency of the nonminimal BRST charge.

Chandia, O., & Vallilo, B. C. (2015). C Ambitwistor pure spinor string in a type II supergravity background. J. High Energy Phys., (6), 15 pp.
Abstract: We construct the ambitwistor pure spinor string in a general type II supergravity background in the semiclassical regime. Almost all supergravity constraints are obtained from nilpotency of the BRST charge and further consistency conditions from additional worldsheet the case of AdS(5) x S (5) background.
